[vorbis-dev] window function

[hkato]

Dear Sebastian and all,

This is a Japanese to live in Japan.
I have a question. 
Ogg's window functon is

f(x)=sin(1/2*pi*sin^2((x+0.5)/n*pi)) for 0 <= x < n

But I cannot understand why this window function satisfys
the equation

f^2(x)+f^2(x+n/2)=2

which is for MDCT's perfect signal reconstruction.

reference:
Analysis/Synthesis Filter Bank Design Based on Time Domain Aliasing Cancellation
John P. Princen, Alan Bernard Bradley
IEEE Transactions on Acoustics,Speech and Signal Processing  vol.ASSP-34,No.5,October 1986 

<p>If you know the reason why,please teach me.

Regards,

Kato

-------------------------------------------------------------------------------------------
>Vorbis Development List, November 2002
>[[vorbis-dev] MDCT-Window still wrong]
>From: Sebastian Gesemann (sgeseman at uni-paderborn.de)
>Date: Wed 13 Nov 2002 - 14:56:39 EST
>
>In vorbis-spec-intro.html, the MDCT-Window is still wrong.
>
>Should be sin(1/2*pi*sin^2((x+0.5)/n*pi))
>for 0 <= x < n
>
>bye,
>Sebastian 

<p>--- >8 ----
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